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Assignments: The Basic Law

The assignment of a right or obligation is a common contractual event under the law and the right to assign (or prohibition against assignments) is found in the majority of agreements, leases and business structural documents created in the United States.

As with many terms commonly used, people are familiar with the term but often are not aware or fully aware of what the terms entail. The concept of assignment of rights and obligations is one of those simple concepts with wide ranging ramifications in the contractual and business context and the law imposes severe restrictions on the validity and effect of assignment in many instances. Clear contractual provisions concerning assignments and rights should be in every document and structure created and this article will outline why such drafting is essential for the creation of appropriate and effective contracts and structures.

The reader should first read the article on Limited Liability Entities in the United States and Contracts since the information in those articles will be assumed in this article.

Basic Definitions and Concepts:

An assignment is the transfer of rights held by one party called the “assignor” to another party called the “assignee.” The legal nature of the assignment and the contractual terms of the agreement between the parties determines some additional rights and liabilities that accompany the assignment. The assignment of rights under a contract usually completely transfers the rights to the assignee to receive the benefits accruing under the contract. Ordinarily, the term assignment is limited to the transfer of rights that are intangible, like contractual rights and rights connected with property. Merchants Service Co. v. Small Claims Court , 35 Cal. 2d 109, 113-114 (Cal. 1950).

An assignment will generally be permitted under the law unless there is an express prohibition against assignment in the underlying contract or lease. Where assignments are permitted, the assignor need not consult the other party to the contract but may merely assign the rights at that time. However, an assignment cannot have any adverse effect on the duties of the other party to the contract, nor can it diminish the chance of the other party receiving complete performance. The assignor normally remains liable unless there is an agreement to the contrary by the other party to the contract.

The effect of a valid assignment is to remove privity between the assignor and the obligor and create privity between the obligor and the assignee. Privity is usually defined as a direct and immediate contractual relationship. See Merchants case above.

Further, for the assignment to be effective in most jurisdictions, it must occur in the present. One does not normally assign a future right; the assignment vests immediate rights and obligations.

No specific language is required to create an assignment so long as the assignor makes clear his/her intent to assign identified contractual rights to the assignee. Since expensive litigation can erupt from ambiguous or vague language, obtaining the correct verbiage is vital. An agreement must manifest the intent to transfer rights and can either be oral or in writing and the rights assigned must be certain.

Note that an assignment of an interest is the transfer of some identifiable property, claim, or right from the assignor to the assignee. The assignment operates to transfer to the assignee all of the rights, title, or interest of the assignor in the thing assigned. A transfer of all rights, title, and interests conveys everything that the assignor owned in the thing assigned and the assignee stands in the shoes of the assignor. Knott v. McDonald’s Corp ., 985 F. Supp. 1222 (N.D. Cal. 1997)

The parties must intend to effectuate an assignment at the time of the transfer, although no particular language or procedure is necessary. As long ago as the case of National Reserve Co. v. Metropolitan Trust Co ., 17 Cal. 2d 827 (Cal. 1941), the court held that in determining what rights or interests pass under an assignment, the intention of the parties as manifested in the instrument is controlling.

The intent of the parties to an assignment is a question of fact to be derived not only from the instrument executed by the parties but also from the surrounding circumstances. When there is no writing to evidence the intention to transfer some identifiable property, claim, or right, it is necessary to scrutinize the surrounding circumstances and parties’ acts to ascertain their intentions. Strosberg v. Brauvin Realty Servs., 295 Ill. App. 3d 17 (Ill. App. Ct. 1st Dist. 1998)

The general rule applicable to assignments of choses in action is that an assignment, unless there is a contract to the contrary, carries with it all securities held by the assignor as collateral to the claim and all rights incidental thereto and vests in the assignee the equitable title to such collateral securities and incidental rights. An unqualified assignment of a contract or chose in action, however, with no indication of the intent of the parties, vests in the assignee the assigned contract or chose and all rights and remedies incidental thereto.

More examples: In Strosberg v. Brauvin Realty Servs ., 295 Ill. App. 3d 17 (Ill. App. Ct. 1st Dist. 1998), the court held that the assignee of a party to a subordination agreement is entitled to the benefits and is subject to the burdens of the agreement. In Florida E. C. R. Co. v. Eno , 99 Fla. 887 (Fla. 1930), the court held that the mere assignment of all sums due in and of itself creates no different or other liability of the owner to the assignee than that which existed from the owner to the assignor.

And note that even though an assignment vests in the assignee all rights, remedies, and contingent benefits which are incidental to the thing assigned, those which are personal to the assignor and for his sole benefit are not assigned. Rasp v. Hidden Valley Lake, Inc ., 519 N.E.2d 153, 158 (Ind. Ct. App. 1988). Thus, if the underlying agreement provides that a service can only be provided to X, X cannot assign that right to Y.

Novation Compared to Assignment:

Although the difference between a novation and an assignment may appear narrow, it is an essential one. “Novation is a act whereby one party transfers all its obligations and benefits under a contract to a third party.” In a novation, a third party successfully substitutes the original party as a party to the contract. “When a contract is novated, the other contracting party must be left in the same position he was in prior to the novation being made.”

A sublease is the transfer when a tenant retains some right of reentry onto the leased premises. However, if the tenant transfers the entire leasehold estate, retaining no right of reentry or other reversionary interest, then the transfer is an assignment. The assignor is normally also removed from liability to the landlord only if the landlord consents or allowed that right in the lease. In a sublease, the original tenant is not released from the obligations of the original lease.

Equitable Assignments:

An equitable assignment is one in which one has a future interest and is not valid at law but valid in a court of equity. In National Bank of Republic v. United Sec. Life Ins. & Trust Co. , 17 App. D.C. 112 (D.C. Cir. 1900), the court held that to constitute an equitable assignment of a chose in action, the following has to occur generally: anything said written or done, in pursuance of an agreement and for valuable consideration, or in consideration of an antecedent debt, to place a chose in action or fund out of the control of the owner, and appropriate it to or in favor of another person, amounts to an equitable assignment. Thus, an agreement, between a debtor and a creditor, that the debt shall be paid out of a specific fund going to the debtor may operate as an equitable assignment.

In Egyptian Navigation Co. v. Baker Invs. Corp. , 2008 U.S. Dist. LEXIS 30804 (S.D.N.Y. Apr. 14, 2008), the court stated that an equitable assignment occurs under English law when an assignor, with an intent to transfer his/her right to a chose in action, informs the assignee about the right so transferred.

An executory agreement or a declaration of trust are also equitable assignments if unenforceable as assignments by a court of law but enforceable by a court of equity exercising sound discretion according to the circumstances of the case. Since California combines courts of equity and courts of law, the same court would hear arguments as to whether an equitable assignment had occurred. Quite often, such relief is granted to avoid fraud or unjust enrichment.

Note that obtaining an assignment through fraudulent means invalidates the assignment. Fraud destroys the validity of everything into which it enters. It vitiates the most solemn contracts, documents, and even judgments. Walker v. Rich , 79 Cal. App. 139 (Cal. App. 1926). If an assignment is made with the fraudulent intent to delay, hinder, and defraud creditors, then it is void as fraudulent in fact. See our article on Transfers to Defraud Creditors .

But note that the motives that prompted an assignor to make the transfer will be considered as immaterial and will constitute no defense to an action by the assignee, if an assignment is considered as valid in all other respects.

Enforceability of Assignments:

Whether a right under a contract is capable of being transferred is determined by the law of the place where the contract was entered into. The validity and effect of an assignment is determined by the law of the place of assignment. The validity of an assignment of a contractual right is governed by the law of the state with the most significant relationship to the assignment and the parties.

In some jurisdictions, the traditional conflict of laws rules governing assignments has been rejected and the law of the place having the most significant contacts with the assignment applies. In Downs v. American Mut. Liability Ins. Co ., 14 N.Y.2d 266 (N.Y. 1964), a wife and her husband separated and the wife obtained a judgment of separation from the husband in New York. The judgment required the husband to pay a certain yearly sum to the wife. The husband assigned 50 percent of his future salary, wages, and earnings to the wife. The agreement authorized the employer to make such payments to the wife.

After the husband moved from New York, the wife learned that he was employed by an employer in Massachusetts. She sent the proper notice and demanded payment under the agreement. The employer refused and the wife brought an action for enforcement. The court observed that Massachusetts did not prohibit assignment of the husband’s wages. Moreover, Massachusetts law was not controlling because New York had the most significant relationship with the assignment. Therefore, the court ruled in favor of the wife.

Therefore, the validity of an assignment is determined by looking to the law of the forum with the most significant relationship to the assignment itself. To determine the applicable law of assignments, the court must look to the law of the state which is most significantly related to the principal issue before it.

Assignment of Contractual Rights:

Generally, the law allows the assignment of a contractual right unless the substitution of rights would materially change the duty of the obligor, materially increase the burden or risk imposed on the obligor by the contract, materially impair the chance of obtaining return performance, or materially reduce the value of the performance to the obligor. Restat 2d of Contracts, § 317(2)(a). This presumes that the underlying agreement is silent on the right to assign.

If the contract specifically precludes assignment, the contractual right is not assignable. Whether a contract is assignable is a matter of contractual intent and one must look to the language used by the parties to discern that intent.

In the absence of an express provision to the contrary, the rights and duties under a bilateral executory contract that does not involve personal skill, trust, or confidence may be assigned without the consent of the other party. But note that an assignment is invalid if it would materially alter the other party’s duties and responsibilities. Once an assignment is effective, the assignee stands in the shoes of the assignor and assumes all of assignor’s rights. Hence, after a valid assignment, the assignor’s right to performance is extinguished, transferred to assignee, and the assignee possesses the same rights, benefits, and remedies assignor once possessed. Robert Lamb Hart Planners & Architects v. Evergreen, Ltd. , 787 F. Supp. 753 (S.D. Ohio 1992).

On the other hand, an assignee’s right against the obligor is subject to “all of the limitations of the assignor’s right, all defenses thereto, and all set-offs and counterclaims which would have been available against the assignor had there been no assignment, provided that these defenses and set-offs are based on facts existing at the time of the assignment.” See Robert Lamb , case, above.

The power of the contract to restrict assignment is broad. Usually, contractual provisions that restrict assignment of the contract without the consent of the obligor are valid and enforceable, even when there is statutory authorization for the assignment. The restriction of the power to assign is often ineffective unless the restriction is expressly and precisely stated. Anti-assignment clauses are effective only if they contain clear, unambiguous language of prohibition. Anti-assignment clauses protect only the obligor and do not affect the transaction between the assignee and assignor.

Usually, a prohibition against the assignment of a contract does not prevent an assignment of the right to receive payments due, unless circumstances indicate the contrary. Moreover, the contracting parties cannot, by a mere non-assignment provision, prevent the effectual alienation of the right to money which becomes due under the contract.

A contract provision prohibiting or restricting an assignment may be waived, or a party may so act as to be estopped from objecting to the assignment, such as by effectively ratifying the assignment. The power to void an assignment made in violation of an anti-assignment clause may be waived either before or after the assignment. See our article on Contracts.

Noncompete Clauses and Assignments:

Of critical import to most buyers of businesses is the ability to ensure that key employees of the business being purchased cannot start a competing company. Some states strictly limit such clauses, some do allow them. California does restrict noncompete clauses, only allowing them under certain circumstances. A common question in those states that do allow them is whether such rights can be assigned to a new party, such as the buyer of the buyer.

A covenant not to compete, also called a non-competitive clause, is a formal agreement prohibiting one party from performing similar work or business within a designated area for a specified amount of time. This type of clause is generally included in contracts between employer and employee and contracts between buyer and seller of a business.

Many workers sign a covenant not to compete as part of the paperwork required for employment. It may be a separate document similar to a non-disclosure agreement, or buried within a number of other clauses in a contract. A covenant not to compete is generally legal and enforceable, although there are some exceptions and restrictions.

Whenever a company recruits skilled employees, it invests a significant amount of time and training. For example, it often takes years before a research chemist or a design engineer develops a workable knowledge of a company’s product line, including trade secrets and highly sensitive information. Once an employee gains this knowledge and experience, however, all sorts of things can happen. The employee could work for the company until retirement, accept a better offer from a competing company or start up his or her own business.

A covenant not to compete may cover a number of potential issues between employers and former employees. Many companies spend years developing a local base of customers or clients. It is important that this customer base not fall into the hands of local competitors. When an employee signs a covenant not to compete, he or she usually agrees not to use insider knowledge of the company’s customer base to disadvantage the company. The covenant not to compete often defines a broad geographical area considered off-limits to former employees, possibly tens or hundreds of miles.

Another area of concern covered by a covenant not to compete is a potential ‘brain drain’. Some high-level former employees may seek to recruit others from the same company to create new competition. Retention of employees, especially those with unique skills or proprietary knowledge, is vital for most companies, so a covenant not to compete may spell out definite restrictions on the hiring or recruiting of employees.

A covenant not to compete may also define a specific amount of time before a former employee can seek employment in a similar field. Many companies offer a substantial severance package to make sure former employees are financially solvent until the terms of the covenant not to compete have been met.

Because the use of a covenant not to compete can be controversial, a handful of states, including California, have largely banned this type of contractual language. The legal enforcement of these agreements falls on individual states, and many have sided with the employee during arbitration or litigation. A covenant not to compete must be reasonable and specific, with defined time periods and coverage areas. If the agreement gives the company too much power over former employees or is ambiguous, state courts may declare it to be overbroad and therefore unenforceable. In such case, the employee would be free to pursue any employment opportunity, including working for a direct competitor or starting up a new company of his or her own.

It has been held that an employee’s covenant not to compete is assignable where one business is transferred to another, that a merger does not constitute an assignment of a covenant not to compete, and that a covenant not to compete is enforceable by a successor to the employer where the assignment does not create an added burden of employment or other disadvantage to the employee. However, in some states such as Hawaii, it has also been held that a covenant not to compete is not assignable and under various statutes for various reasons that such covenants are not enforceable against an employee by a successor to the employer. Hawaii v. Gannett Pac. Corp. , 99 F. Supp. 2d 1241 (D. Haw. 1999)

It is vital to obtain the relevant law of the applicable state before drafting or attempting to enforce assignment rights in this particular area.

Conclusion:

In the current business world of fast changing structures, agreements, employees and projects, the ability to assign rights and obligations is essential to allow flexibility and adjustment to new situations. Conversely, the ability to hold a contracting party into the deal may be essential for the future of a party. Thus, the law of assignments and the restriction on same is a critical aspect of every agreement and every structure. This basic provision is often glanced at by the contracting parties, or scribbled into the deal at the last minute but can easily become the most vital part of the transaction.

As an example, one client of ours came into the office outraged that his co venturer on a sizable exporting agreement, who had excellent connections in Brazil, had elected to pursue another venture instead and assigned the agreement to a party unknown to our client and without the business contacts our client considered vital. When we examined the handwritten agreement our client had drafted in a restaurant in Sao Paolo, we discovered there was no restriction on assignment whatsoever…our client had not even considered that right when drafting the agreement after a full day of work.

One choses who one does business with carefully…to ensure that one’s choice remains the party on the other side of the contract, one must master the ability to negotiate proper assignment provisions.

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Validity of a Contract Assignment

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  What Is a Contract?

A contract is a legally binding arrangement between two or more parties. A contract supplies particulars of what the parties agree to perform or exchange. A contract may be in written or oral form. In most cases, to be legally binding, a contract must be in writing and signed by all parties concerned.

Courts typically require three things for a contract to be enforceable:

  • Mutual assent, or agreement to the contract terms;
  • A valid offer and acceptance; and
  • Consideration.

Contracts are deemed the foundation of the business world. They may be easy or very complicated. Examples of contracts include employment contracts, real estate purchase agreements, and insurance arrangements.

Contracts must be entered into by all parties freely. All parties signing the contract must do so of their own free will and not under duress . Contracts can be used whenever parties want to document an agreement to ensure all parties’ rights are covered.

Drafting a contract refers to writing the terms and details of a contract to specify and summarize the legal responsibilities of all parties to the contract. This permits all parties to the contract to understand their duties and legal obligations to one another clearly.

Anyone can draft a contract, but it would be in the best interest of all parties involved to have an attorney draft a contract, particularly if it is intricate or complicated. For instance, a real estate agreement often involves multiple aspects, multiple parties, and intricate land descriptions. To ensure your sale or purchase, financial investment, and rights are shielded, having an attorney draft this type of agreement would be preferable.

A contract will also deliver sections outlining whether or not it may be canceled and how to revoke it. The agreement will also outline the results if a party breaches the contract terms. A well-written contract will contain explicit definitions of what comprises a breach of the agreement so all parties can support their responsibilities.

What Are the Elements of a Legally Binding Contract?

What is a contract assignment, when is a contract assignment valid, are there any limitations on contract assignments, what does a contract lawyer do, do i need a lawyer for help with a contract assignment.

To be legally binding, a contract is required to include certain elements. Some contracts must be in writing to be valid, such as contracts for money over $500.00. A contract must be created for a lawful purpose. For instance, an individual cannot contract to perpetrate a crime. It is essential to be familiar with the requirements of a valid contract.

A valid contract must include:

  • An acceptance of the offer;
  • A promise to perform;
  • A valuable consideration ;
  • A date, a time window, or an event when the performance must be satisfied;
  • Terms and conditions of the performance; and
  • Performance.

The offer and acceptance segments of a contract are also known as the “meeting of the minds” or mutual agreement of the parties. All parties’ signing of the contract is often used to prove that agreement. In some circumstances, offers may have an expiration period, where the offer is open for a reasonable time. Some offers may not have a time limitation. Offers can be withdrawn until the time of acceptance.

Acceptance happens when the parties agree to the terms of the offer. If a modification is made to the offer terms, it would be deemed a counteroffer. Different states have various regulations in this area of contracts, so it is essential to review local laws.

For a contract to be proper, consideration must be supplied. When both parties agree to provide something of value in exchange for a benefit, consideration ensues. For instance, consideration must be something of value and can include money, a car, or manual labor.

For a contract to be proper, all parties must be legally competent . Some people cannot enter into contracts, such as minors or the mentally impaired. A party must be of sound mind and not under the influence of drugs or alcohol at contracting. All parties to a contract must be free from coercion at contracting. Contracts will be proclaimed void if there is a mistake, coercion, or deception by one or more parties.

In a contracts setting, an “assignment” refers to transferring benefits or rights granted by the contract terms from the receiving party to a different party. Therefore, contract assignments bring an additional party to the existent contract parties.

An illustration of this is where a contractor assigns their right to payments to another party. The other party would then be entitled to fees for the contractor’s work. This is different from a contract delegation , which transmits obligations rather than rights to another party. Assignment usually ensues because it involves some potential for profit for the party making the assignment.

Contract rights and benefits can lawfully be assigned so long as no prior agreement prohibits an assignment. All required is for the assigning party (the assignor) to agree with the assignee (the third party recipient) that they will be transmitting their rights to them. The original party rendering the payment (the “obligor”) doesn’t usually need to be told that an assignment has occurred.

When assigning contract rights to an assignee, an oral agreement may suffice. Yet, as in any deal, it’s best to reduce the assignment to writing so that the parties have a record of the agreement in the future.

The validity of an assignment may depend on the kind of language used in the written agreement. It needs to be in the present tense. That is, the assignor must state, “I am assigning my contract rights to X party,” rather than “I will be assigning my contract rights to X party”

Typically, the parties are free to make assignments, so long as they stick to the following rules:

  • The assignment should be permitted according to local, state, and federal regulations (for instance, some states make it unlawful to allocate wages to another individual)
  • The assignment should only shield present transfers of rights and not future transfers.
  • If the contract contains a specific “no-assignment” condition or clause, then an assignment can’t be made (if one is made in such a case, it may comprise a breach of contract)
  • The assignment should not substantially change the contract or subject the obligor to losses or financial risks.

Also, any time an assignment is made, the assignor implicitly warrants that the rights are accurate, that they own the assigned rights, and won’t interfere with the party’s new claim to the rights. Assignments become proper when formed (even if the recipient is not yet cognizant of the assignment).

The tasks and duties of a contract attorney include preparing contracts, checking contracts, and ensuring their clients’ rights are safeguarded. Contract attorneys are experienced in the prerequisites of contracts and how to make sure they will be enforceable. These types of arrangements must often include certain legal aspects and language.

A contract attorney will help a company or person include the essential terms needed for their business needs and include any legal language the person may not know is required.

Contract assignments can often become somewhat difficult, as they involve the privileges and responsibilities of many different parties. It’s in your best interests to speak with a contracts lawyer if you have any questions about a contract assignment.

Your lawyer will be able to examine the contract and the assignment terms to decide what your legal rights are. In the event of a lawsuit, your attorney can help represent your interests in court.

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Legal Assignment: Everything You Need to Know

A legal assignment occurs when a party assigns their contractual rights to a third party. 3 min read updated on February 01, 2023

A legal assignment occurs when a party assigns their contractual rights to a third party. The benefit that the issuing party would have received from the contract is now assigned to the third party. The party appointing their rights is referred to as the assignor, while the party obtaining the rights is the assignee.

Assignment of Contract

A legal assignment occurs when:

  • The rights in personal or real property are transferred from one party to another
  • The transfer also gives the new owner the rights to the property that the prior owner held prior to the transfer occurring

In the Purman Estate case, the court stated that a legal assignment is a transfer of property, or of some right or interest, from one person to another. It also stated that it must be the proper transfer of one whole interest in that property.

An assignment of rights occurs when an assignor gives up or transfers their rights of a future benefit to another party. In other words, an assignment is the act of one party transferring, vesting, or causing to vest their interest in a property to another party. A valid legal assignment only occurs when all underlying elements of a lawfully binding contract are included in it, including intent. A trial court can determine if an assignment has occurred. To prevent disputes or miscommunications, it's important that the subject matter is clearly identified in the assignment.

A contract assignment occurs when a party assigns their contractual rights to a third party. The benefit the issuing party would have received from the contract is now assigned to the third party. The party appointing their rights is referred to as the assignor, while the party obtaining the rights is the assignee. Essentially, the assignor prefers that the assignee reverses roles and assumes the contractual rights and obligations as stated in the contract. Before this can occur, all parties to the original contract must be notified.

How Assignments Work

The specific language used in the contract will determine how the assignment plays out. For example , one contract may prohibit assignment, while another contract may require that all parties involved agree to it before proceeding. Remember, an assignment of contract does not necessarily alleviate an assignor from all liability. Many contracts include an assurance clause guaranteeing performance. In other words, the initial parties to the contract guarantee that the assignee will achieve the desired goal.

When Assignments Will Not Be Enforced

The following situations indicate when an assignment of a contract is not enforced:

  • The contract specifically prohibits assignment
  • The assignment drastically changes the expected outcome
  • The assignment is against public policy or illegal

Delegation vs. Assignment

Occasionally, one party in a contract will desire to pass on or delegate their responsibility to a third party without creating an assignment contract. Some duties are so specific in nature that they cannot be delegated. Adding a clause in the contract to prevent a party from delegating their responsibilities and duties is highly recommended.

Three Steps to Follow if You Want to Assign a Contract

There are three main steps to take if you're looking to assign a contract:

  • Make sure the current contract does not contain an anti-assignment clause
  • Officially execute the assignment by transferring the parties' obligations and rights
  • Notify the obligor of the changes made

Once the obligor is notified, the assignor will effectively be relieved of liability.

Anti-Assignment Clauses

If you'd prefer not to allow the party you're doing business with to assign a contract, you may be able to prevent this from occurring by clearly stating anti-assignment clauses in the original contract. The three most common anti-assignment clauses are:

  • Consent required for assignment
  • Consent not needed for new owners or affiliates
  • Consent not unreasonably withheld

Based on these three clauses, no party in the contract is allowed to delegate or assign any obligations or rights without prior written consent from the other parties. Any delegation or assignment in violation of this passage shall be deemed void. It is not possible to write an anti-assignment clause that goes against an assignment that is issued or ordered by a court.

If you need help with a legal assignment, you can  post your job  on UpCounsel's marketplace. UpCounsel accepts only the top 5 percent of lawyers to its site. Lawyers on UpCounsel come from law schools such as Harvard Law and Yale Law and average 14 years of legal experience, including work with or on behalf of companies like Google, Menlo Ventures, and Airbnb. 

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  • Assignment Law
  • Assignment Contract Law
  • Assignment of Rights and Obligations Under a Contract
  • Assignment of Rights Example
  • Consent to Assignment
  • Assignment Legal Definition
  • What Is the Definition of Assigns
  • Delegation vs Assignment
  • Assignment Of Contracts
  • Assignment of Contract Rights

3.1 Introduction

Validity, satisfiability, falsifiability, and unsatisfiability are properties of individual sentences or sets on sentences. In Logic, we are sometimes more concerned with relationships between sentences. In this chapter, we look at three such relationships - logical entailment, logical equivalence, and logical consistency. We conclude with a look at the relationship between these logical relationships and the notion of satisfiability.

Satisfaction is a relationship between specific sentences and specific truth assignments. In Logic, we are sometimes more interested in the properties of sentences that hold across truth assignments. In particular, the notion of satisfaction imposes a classification of sentences in a language based on whether there are truth assignments that satisfy that sentence.

Satisfaction is a relationship between specific sentences and specific truth assignments. In Logic, we are usually more interested in properties and relationships of sentences that hold across all truth assignments. We begin this chapter with a look at logical properties of individual sentences (as opposed to relationships among sentences) - validity, contingency, and unsatisfiability. We then look at three types of logical relationship between sentences - logical entailment, logical equivalence, and logical consistency. We conclude with a discussion of the connections between the logical properties of individual sentences and logical relationships between sentences.

3.2 Logical Properties

In the preceding chapter, we saw that some sentences are true in some truth assignments and false in others. However, this is not always the case. There are sentences that are always true and sentences that are always false as well as sentences that are sometimes true and sometimes false. This leads to a partition of sentences into three disjoint categories.

A sentence is valid if and only if it is satisfied by every truth assignment. For example, the sentence ( p ∨ ¬ p ) is valid. If a truth assignment makes p true, then the first disjunct is true and the disjunction as a whole true. If a truth assignment makes p false, then the second disjunct is true and the disjunction as a whole is true.

A sentence is unsatisfiable if and only if it is not satisfied by any truth assignment. For example, the sentence ( p ∧ ¬ p ) is unsatisfiable. No matter what truth assignment we take, the sentence is always false. The argument is analogous to the argument in the preceding paragraph.

Finally, a sentence is contingent if and only if there is some truth assignment that satisfies it and some truth assignment that falsifies it. For example, the sentence ( p ∧ q ) is contingent. If p and q are both true, it is true. If p and q are both false, it is false.

In one sense, valid sentences and unsatisfiable sentences are useless. Valid sentences do not rule out any possible truth assignments, and unsatisfiable sentences rule out all truth assignments. Thus, they tell us nothing about the world. In this regard, contingent sentences are the most useful. On the other hand, from a logical perspective, valid and unsatisfiable sentences are useful in that, as we shall see, they serve as the basis for legal transformations that we can perform on other logical sentences.

For many purposes, it is useful to group validity, contingency, and unsatisfiability into two groups. We say that a sentence is satisfiable if and only if it is valid or contingent. In other words the sentence is satisfied by at least one truth assignment. We say that a sentence is falsifiable if and only if it is unsatisfiable or contingent. In other words, the sentence is falsified by at least one truth assignment.

3.3 Logical Equivalence

Intuitively, we think of two sentences as being equivalent if they say the same thing, i.e. they are true in exactly the same worlds. More formally, we say that a sentence φ is logically equivalent to a sentence ψ if and only if every truth assignment that satisfies φ satisfies ψ and every truth assignment that satisfies ψ satisfies φ.

The sentence ¬( p ∨ q ) is logically equivalent to the sentence (¬ p ∧ ¬ q ). If p and q are both true, then both sentences are false. If either p is true or q is true, then the disjunction in the first sentence is true and the sentence as a whole false. Similarly, if either p is true or q is true, then one of the conjuncts in the second sentence is false and so the sentence as a whole is false. Since both sentences are satisfied by the same truth assignments, they are logically equivalent.

By contrast, the sentences ( p ∧ q ) and ( p ∨ q ) are not logically equivalent. The first is false when p is true and q is false, while in this situation the disjunction is true. Hence, they are not logically equivalent.

One way of determining whether or not two sentences are logically equivalent is to check the truth table for the proposition constants in the language. This is called the truth table method. (1) First, we form a truth table for the proposition constants and add a column for each of the sentences. (2) We then evaluate the two expressions. (3) Finally, we compare the results. If the values for the two sentences are the same in every case, then the two sentences are logically equivalent; otherwise, they are not.

As an example, let's use this method to show that ¬( p ∨ q ) is logically equivalent to (¬ p ∧ ¬ q ). We set up our truth table, add a column for each of our two sentences, and evaluate them for each truth assignment. Having done so, we notice that every row that satisfies the first sentence also satisfies the second. Hence, the sentences are logically equivalent.

Now, let's do the same for ( p ∧ q ) and ( p ∨ q ). We set up our table as before and evaluate our sentences. In this case, there is only one row that satisfies first sentence while three rows satisfy the second. Consequently, they are not logically equivalent.

One of the interesting properties of logical equivalence is substitutability. If a sentence φ is logically equivalent to a sentence ψ, then we can substitute φ for ψ in any Propositional Logic sentence and the result will be logically equivalent to the original sentence. (Note that this is not quite true in Relational Logic, as we shall see when we cover that logic.)

3.4 Logical Entailment

We say that a sentence φ logically entails a sentence ψ (written φ ⊨ ψ) if and only if every truth assignment that satisfies φ also satisfies ψ. More generally, we say that a set of sentences Δ logically entails a sentence ψ (written Δ ⊨ ψ) if and only if every truth assignment that satisfies all of the sentences in Δ also satisfies ψ.

For example, the sentence p logically entails the sentence ( p ∨ q ). Since a disjunction is true whenever one of its disjuncts is true, then ( p ∨ q ) must be true whenever p is true. On the other hand, the sentence p does not logically entail ( p ∧ q ). A conjunction is true if and only if both of its conjuncts are true, and q may be false. Of course, any set of sentences containing both p and q does logically entail ( p ∧ q ).

Note that the relationship of logical entailment is a purely logical one. Even if the premises of a problem do not logically entail the conclusion, this does not mean that the conclusion is necessarily false, even if the premises are true. It just means that it is possible that the conclusion is false.

Once again, consider the case of ( p ∧ q ). Although p does not logically entail this sentence, it is possible that both p and q are true and, therefore, ( p ∧ q ) is true. However, the logical entailment does not hold because it is also possible that q is false and, therefore, ( p ∧ q ) is false.

Note also that logical entailment is not the same as logical equivalence. The sentence p logically entails ( p ∨ q ), but ( p ∨ q ) does not logically entail p . Logical entailment is not analogous to arithmetic equality; it is closer to arithmetic inequality.

As with logical equivalence, we can use truth tables to determine whether or not a set of premises logically entails a possible conclusion by checking the truth table for the proposition constants in the language. (1) We form a truth table for the proposition constants and add a column for the premises and a column for the conclusion. (2) We then evaluate the premises. (3) We evaluate the conclusion. (4) Finally, we compare the results. If every row that satisfies the premises also satisfies the conclusion, then the premises logically entail the conclusion.

As an example, let's use this method to show that p logically entails ( p ∨ q ). We set up our truth table and add a column for our premise and a column for our conclusion. In this case the premise is just p and so evaluation is straightforward; we just copy the column. The conclusion is true if and only if p is true or q is true. Finally, we notice that every row that satisfies the premise also satisfies the conclusion.

Now, let's look at the problem of determining whether the set of propositions { p , q } logically entails ( p ∧ q ). Here we set up our table as before, but this time we have two premises to satisfy. Only one truth assignment satisfies both premises, and this truth assignment also satisfies the conclusion; hence in this case logical entailment does hold.

As a final example, let's return to the love life of the fickle Mary. Here is the problem from the course introduction. We know ( p ⇒ q ), i.e. if Mary loves Pat, then Mary loves Quincy. We know ( m ⇒ p ∨ q ), i.e. if it is Monday, then Mary loves Pat or Quincy. Let's confirm that, if it is Monday, then Mary loves Quincy. We set up our table and evaluate our premises and our conclusion. Both premises are satisfied by the truth assignments on rows 1, 3, 5, 7, and 8; and we notice that those truth assignments make the conclusion true. Hence, the logical entailment holds.

3.5 Logical Consistency

A sentence φ is consistent with a sentence ψ if and only if there is a truth assignment that satisfies both φ and ψ. A sentence ψ is consistent with a set of sentences Δ if and only if there is a truth assignment that satisfies both Δ and ψ.

For example, the sentence ( p ∨ q ) is consistent with the sentence (¬ p ∨ ¬ q ). However, it is not consistent with (¬ p ∧ ¬ q ).

As with logical equivalence and logical entailment, we can use the truth table method to determine logical consistency. The following truth table shows all truth assignments for the propositional constants in the examples just mentioned. The third column shows the truth values for the first sentence; the fourth column shows the truth values for the second sentence, and the fifth column shows the truth values for the third sentence. The second and third truth assignments here make ( p ∨ q ) true and also (¬ p ∨ ¬ q ); hence ( p ∨ q ) and (¬ p ∨ ¬ q ) are consistent. By contrast, none of the truth assignments that makes ( p ∨ q ) true makes (¬ p ∧ ¬ q ) true; hence, they are not consistent.

The distinction between entailment and consistency is a subtle one and deserves some attention. Just because two sentences are consistent does not mean that they are logically equivalent or that either sentence logically entails the other.

Consider the sentences in the previous example. As we have seen, the first sentence and the second sentence are logically consistent, but they are clearly not logically equivalent and neither sentence logically entails the other.

Conversely, if one sentence logically entails another this does not necessarily mean that the sentences are consistent. This situation occurs when one of the sentences is unsatisfiable. If a sentence is unsatisfiable, there are no truth assignments that satisfy it. So, by definition, every truth assignment that satisfies the sentence (there are none) trivially satisfies the other sentence.

An interesting consequence of this fact is that any unsatisfiable sentence or set of sentences logically entails everything . Weird fact, but it follows directly from our definitions. And it makes clear why we want to avoid unsatisfiable sets of sentences in logical reasoning.

3.6 Connections Between Properties and Relationships

Before we end this chapter, it is worth noting that there are some strong connections between logical properties like validity and satisfiability and the logical relationships introduced in the preceding three sections.

First of all, there is a connection between the logical equivalence of two sentences and the validity of the biconditional sentence built from the two sentences. In particular, we have the following theorem expressing this connection.

Equivalence Theorem : A sentence φ and a sentence ψ are logically equivalent if and only if the sentence (φ ⇔ ψ) is valid.

There is a similar connection between logical entailment between two sentences and the validity of the corresponding implication. And there is a natural extension to cases of logical entailment involving finite sets of sentences. The following theorem summarizes these results.

Deduction Theorem : A sentence φ logically entails a sentence ψ if and only if (φ ⇒ ψ) is valid. More generally, a finite set of sentences {φ 1 , ... , φ n } logically entails φ if and only if the compound sentence (φ 1 ∧ ... ∧ φ n ⇒ φ) is valid.

If a sentence φ logically entails a sentence ψ, it means that any truth assignment that satisfies φ also satisfies ψ. Looking at the semantics of implications, we see that an implication is true if and only if every truth assignment that makes the antecedent true also makes the consequent true. Consequently, logical entailment holds exactly when the corresponding implication is valid.

There is also a connection between logical entailment and unsatisfiability. In particular, if a set Δ of sentences logically entails a sentence φ, then Δ together with the negation of φ must be unsatisfiable. The reverse is also true.

Unsatisfiability Theorem : A set Δ of sentences logically entails a sentence φ if and only if the set of sentences Δ ∪ {¬φ} is unsatisfiable.

Suppose that Δ logically entails φ. If a truth assignment satisfies Δ, then it must also satisfy φ. But then it cannot satisfy ¬φ. Therefore, Δ ∪ {¬φ} is unsatisfiable. Suppose that Δ∪{¬φ} is unsatisfiable. Then every truth assignment that satisfies Δ must fail to satisfy ¬φ, i.e. it must satisfy φ. Therefore, Δ must logically entail φ.

An interesting consequence of this result is that we can determine logical entailment by checking for unsatisfiability. This turns out to be useful in various logical proof methods, as described in the following chapters.

Finally, consider the definition of logical consistency. A sentence φ is logically consistent with a sentence ψ if and only if there is a truth assignment that satisfies both φ and ψ. This is equivalent to saying that the sentence (φ ∧ ψ) is satisfiable.

Consistency Theorem : A sentence φ is logically consistent with a sentence ψ if and only if the sentence (φ ∧ ψ) is satisfiable. More generally, a sentence φ is logically consistent with a finite set of sentences {φ 1 , ... , φ n } if and only if the compound sentence (φ 1 ∧ ... ∧ φ n ∧ φ) is satisfiable.

In thinking about these various connections, the main thing to keep in mind is that logical properties and logical relationships are metalevel. They are things we assert in talking about logical sentences; they are not sentences within our formal language. By contrast, implications and biconditionals and conjunctions are statements within our formal language; they are not metalevel statements. What the preceding paragraphs tell us is that we can implicitly express some logical relationships within our formal language by writing the corresponding biconditionals and implications and conjunctions and checking for the logical properties of these sentences.

3.7 Equivalence Rewritings

The connections described in the preceding section are useful in solving logical problems because they allow us to transform problems of one type into problems of another type. For example, if we needed to determine the validity of a sentence of the form (φ => ψ), the deduction theorem tells us that we could instead solve the equivalent problem of determining whether φ logically entails ψ. In making this determination, we need to consider only those interpretations that make φ true and we can ignore all of the other interpretations. The upshot is that solving the equivalent problem can be easier than solving the original.

The idea of problem transformation can also be used to transform problems of one type into equivalent problems of the same type. The trick is to rewrite the sentences involved in the problem into logically equivalent sentences. Suppose we wanted to know whether a complex sentence like ((¬ p ∨ q ) ⇒ ( p ⇒ q )) ∧ q is valid, contingent, or unsatisfiable. Since (¬ p ∨ q ) is logically equivalent to ( p ⇒ q ), we can rewrite the given sentence as (( p ⇒ q ) ⇒ ( p ⇒ q )) ∧ q . The first conjunct is clearly valid; the second is contingent; and so the sentence as whole must be contingent.

The following is a list of logical equivalences that can be used in rewriting sentences as logically equivalent sentences.

Of course, there are many more such equivalences. In fact, there are infinitely many. The ones listed here are the most common and the simplest to apply. Moreover, as we shall see later, they are also the basis for the conversion of sentences to clausal form .

The idea of rewriting sentences as logically equivalent sentences can also be applied to sets. We can transform the individual sentences in the sets; and, in some cases, we can add or delete sentences. For example, we can replace the set { p , p ⇒ q } with the set { p , q }, since they are logically equivalent.

As we shall see in the next two chapters, proofs are, in a way, a special case of this idea (one where we add sentences but do not delete sentences). For example, to prove a conclusion in the Fitch system (described in the next chapter), we start with our set of premises and incrementally add logical consequences until we produce a set containing the desired conclusion. The resolution method (described later) is analogous; to show that a set of sentences is unsatisfiable, we start with a set of premises and add conclusions until we obtain a direct contradiction.

A sentence is valid if and only if it is satisfied by every truth assignment. A sentence is unsatisfiable if and only if it is not satisfied by any truth assignment. A sentence is contingent if and only if it is both satisfiable and falsifiable, i.e. it is neither valid nor unsatisfiable. A sentence is satisfiable if and only if it is either valid or contingent. A sentence is falsifiable if and only if it is unsatisfiable or contingent. A sentence φ is logically equivalent to a sentence ψ if and only if every truth assignment that satisfies φ satisfies ψ and every truth assignment that satisfies ψ satisfies φ. A set of sentences Δ logically entails a sentence φ (written Δ ⊨ φ) if and only if every truth assignment that satisfies Δ also satisfies φ. A sentence φ is consistent with a set of sentences Δ if and only if there is a truth assignment that satisfies both Δ and φ. The Equivalence Theorem states that sentence φ and a sentence ψ are logically equivalent if and only the sentence (φ ⇔ ψ) is valid. The Deduction Theorem states that a sentence φ logically entails a sentence ψ if and only the sentence (φ ⇒ ψ) is valid. More generally, a finite set of sentences {φ 1 , ... , φ n } logically entails φ if and only if the compound sentence (φ 1 ∧ ... ∧ φ 1 ⇒ φ) is valid. The Unsatisfiability Theorem states that a set Δ of sentences logically entails a sentence φ if and only if the set of sentences Δ ∪ {¬φ} is unsatisfiable. The Consistency Theorem states that a sentence φ is consistent with a set of sentences Δ if and only if the set of sentences Δ ∪ {φ} is satisfiable. A sentence φ is consistent with a set of sentences {φ 1 , ... , φ n } if and only if the compound sentence (φ 1 ∧ ... ∧ φ 1 ∧ φ) is satisfiable. Finally, a consequence of our definitions - any unsatisfiable set of sentences logically entails everything.

Exercise 3.1: Say whether each of the following sentences is valid, contingent, or unsatisfiable.

Exercise 3.2: For each of the following pairs of sentences, determine whether or not the sentences are logically equivalent.

Exercise 3.3: Use the Truth Table Method to answer the following questions about logical entailment.

Exercise 3.4: Let Γ and Δ be sets of sentences in Propositional Logic, and let φ and ψ be individual sentences in Propositional Logic. State whether each of the following statements is true or false.

Exercise 3.5: In each of the following cases, determine whether the given individual sentence is consistent with the given set of sentences.

Exercise 3.6: Logical equivalence, logical entailment, and logical consistency are related to each other in interesting ways, but they are not identical. Answer the following true or false questions about the relationships between these concepts.

Assignment of Contract

Jump to section, what is an assignment of contract.

An assignment of contract is a legal term that describes the process that occurs when the original party (assignor) transfers their rights and obligations under their contract to a third party (assignee). When an assignment of contract happens, the original party is relieved of their contractual duties, and their role is replaced by the approved incoming party.

How Does Assignment of Contract Work?

An assignment of contract is simpler than you might think.

The process starts with an existing contract party who wishes to transfer their contractual obligations to a new party.

When this occurs, the existing contract party must first confirm that an assignment of contract is permissible under the legally binding agreement . Some contracts prohibit assignments of contract altogether, and some require the other parties of the agreement to agree to the transfer. However, the general rule is that contracts are freely assignable unless there is an explicit provision that says otherwise.

In other cases, some contracts allow an assignment of contract without any formal notification to other contract parties. If this is the case, once the existing contract party decides to reassign his duties, he must create a “Letter of Assignment ” to notify any other contract signers of the change.

The Letter of Assignment must include details about who is to take over the contractual obligations of the exiting party and when the transfer will take place. If the assignment is valid, the assignor is not required to obtain the consent or signature of the other parties to the original contract for the valid assignment to take place.

Check out this article to learn more about how assigning a contract works.

Contract Assignment Examples

Contract assignments are great tools for contract parties to use when they wish to transfer their commitments to a third party. Here are some examples of contract assignments to help you better understand them:

Anna signs a contract with a local trash company that entitles her to have her trash picked up twice a week. A year later, the trash company transferred her contract to a new trash service provider. This contract assignment effectively makes Anna’s contract now with the new service provider.

Hasina enters a contract with a national phone company for cell phone service. The company goes into bankruptcy and needs to close its doors but decides to transfer all current contracts to another provider who agrees to honor the same rates and level of service. The contract assignment is completed, and Hasina now has a contract with the new phone company as a result.

Here is an article where you can find out more about contract assignments.

an assignment is valid only if

Assignment of Contract in Real Estate

Assignment of contract is also used in real estate to make money without going the well-known routes of buying and flipping houses. When real estate LLC investors use an assignment of contract, they can make money off properties without ever actually buying them by instead opting to transfer real estate contracts .

This process is called real estate wholesaling.

Real Estate Wholesaling

Real estate wholesaling consists of locating deals on houses that you don’t plan to buy but instead plan to enter a contract to reassign the house to another buyer and pocket the profit.

The process is simple: real estate wholesalers negotiate purchase contracts with sellers. Then, they present these contracts to buyers who pay them an assignment fee for transferring the contract.

This process works because a real estate purchase agreement does not come with the obligation to buy a property. Instead, it sets forth certain purchasing parameters that must be fulfilled by the buyer of the property. In a nutshell, whoever signs the purchase contract has the right to buy the property, but those rights can usually be transferred by means of an assignment of contract.

This means that as long as the buyer who’s involved in the assignment of contract agrees with the purchasing terms, they can legally take over the contract.

But how do real estate wholesalers find these properties?

It is easier than you might think. Here are a few examples of ways that wholesalers find cheap houses to turn a profit on:

  • Direct mailers
  • Place newspaper ads
  • Make posts in online forums
  • Social media posts

The key to finding the perfect home for an assignment of contract is to locate sellers that are looking to get rid of their properties quickly. This might be a family who is looking to relocate for a job opportunity or someone who needs to make repairs on a home but can’t afford it. Either way, the quicker the wholesaler can close the deal, the better.

Once a property is located, wholesalers immediately go to work getting the details ironed out about how the sale will work. Transparency is key when it comes to wholesaling. This means that when a wholesaler intends to use an assignment of contract to transfer the rights to another person, they are always upfront about during the preliminary phases of the sale.

In addition to this practice just being good business, it makes sure the process goes as smoothly as possible later down the line. Wholesalers are clear in their intent and make sure buyers know that the contract could be transferred to another buyer before the closing date arrives.

After their offer is accepted and warranties are determined, wholesalers move to complete a title search . Title searches ensure that sellers have the right to enter into a purchase agreement on the property. They do this by searching for any outstanding tax payments, liens , or other roadblocks that could prevent the sale from going through.

Wholesalers also often work with experienced real estate lawyers who ensure that all of the legal paperwork is forthcoming and will stand up in court. Lawyers can also assist in the contract negotiation process if needed but often don’t come in until the final stages.

If the title search comes back clear and the real estate lawyer gives the green light, the wholesaler will immediately move to locate an entity to transfer the rights to buy.

One of the most attractive advantages of real estate wholesaling is that very little money is needed to get started. The process of finding a seller, negotiating a price, and performing a title search is an extremely cheap process that almost anyone can do.

On the other hand, it is not always a positive experience. It can be hard for wholesalers to find sellers who will agree to sell their homes for less than the market value. Even when they do, there is always a chance that the transferred buyer will back out of the sale, which leaves wholesalers obligated to either purchase the property themselves or scramble to find a new person to complete an assignment of contract with.

Learn more about assignment of contract in real estate by checking out this article .

Who Handles Assignment of Contract?

The best person to handle an assignment of contract is an attorney. Since these are detailed legal documents that deal with thousands of dollars, it is never a bad idea to have a professional on your side. If you need help with an assignment of contract or signing a business contract , post a project on ContractsCounsel. There, you can connect with attorneys who know everything there is to know about assignment of contract amendment and can walk you through the whole process.

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Understanding an assignment and assumption agreement

Need to assign your rights and duties under a contract? Learn more about the basics of an assignment and assumption agreement.

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by   Belle Wong, J.D.

Belle Wong, is a freelance writer specializing in small business, personal finance, banking, and tech/SAAS. She ...

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Updated on: January 22, 2024 · 3min read

The assignment and assumption agreement

The basics of assignment and assumption, filling in the assignment and assumption agreement.

While every business should try its best to meet its contractual obligations, changes in circumstance can happen that could necessitate transferring your rights and duties under a contract to another party who would be better able to meet those obligations.

Person presenting documents to another person who is signing them

If you find yourself in such a situation, and your contract provides for the possibility of assignment, an assignment and assumption agreement can be a good option for preserving your relationship with the party you initially contracted with, while at the same time enabling you to pass on your contractual rights and duties to a third party.

An assignment and assumption agreement is used after a contract is signed, in order to transfer one of the contracting party's rights and obligations to a third party who was not originally a party to the contract. The party making the assignment is called the assignor, while the third party accepting the assignment is known as the assignee.

In order for an assignment and assumption agreement to be valid, the following criteria need to be met:

  • The initial contract must provide for the possibility of assignment by one of the initial contracting parties.
  • The assignor must agree to assign their rights and duties under the contract to the assignee.
  • The assignee must agree to accept, or "assume," those contractual rights and duties.
  • The other party to the initial contract must consent to the transfer of rights and obligations to the assignee.

A standard assignment and assumption contract is often a good starting point if you need to enter into an assignment and assumption agreement. However, for more complex situations, such as an assignment and amendment agreement in which several of the initial contract terms will be modified, or where only some, but not all, rights and duties will be assigned, it's a good idea to retain the services of an attorney who can help you draft an agreement that will meet all your needs.

When you're ready to enter into an assignment and assumption agreement, it's a good idea to have a firm grasp of the basics of assignment:

  • First, carefully read and understand the assignment and assumption provision in the initial contract. Contracts vary widely in their language on this topic, and each contract will have specific criteria that must be met in order for a valid assignment of rights to take place.
  • All parties to the agreement should carefully review the document to make sure they each know what they're agreeing to, and to help ensure that all important terms and conditions have been addressed in the agreement.
  • Until the agreement is signed by all the parties involved, the assignor will still be obligated for all responsibilities stated in the initial contract. If you are the assignor, you need to ensure that you continue with business as usual until the assignment and assumption agreement has been properly executed.

Unless you're dealing with a complex assignment situation, working with a template often is a good way to begin drafting an assignment and assumption agreement that will meet your needs. Generally speaking, your agreement should include the following information:

  • Identification of the existing agreement, including details such as the date it was signed and the parties involved, and the parties' rights to assign under this initial agreement
  • The effective date of the assignment and assumption agreement
  • Identification of the party making the assignment (the assignor), and a statement of their desire to assign their rights under the initial contract
  • Identification of the third party accepting the assignment (the assignee), and a statement of their acceptance of the assignment
  • Identification of the other initial party to the contract, and a statement of their consent to the assignment and assumption agreement
  • A section stating that the initial contract is continued; meaning, that, other than the change to the parties involved, all terms and conditions in the original contract stay the same

In addition to these sections that are specific to an assignment and assumption agreement, your contract should also include standard contract language, such as clauses about indemnification, future amendments, and governing law.

Sometimes circumstances change, and as a business owner you may find yourself needing to assign your rights and duties under a contract to another party. A properly drafted assignment and assumption agreement can help you make the transfer smoothly while, at the same time, preserving the cordiality of your initial business relationship under the original contract.

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PHIL102: Introduction to Critical Thinking and Logic

an assignment is valid only if

Truth Tables

Read these sections to learn how to interpret, make, and apply truth tables to sentential logic formulas, note conditional statements in sentential logic, and translate the word "unless" into sentential logic. Be sure to note the difference between an antecedent and a consequent and between a necessary and sufficient condition.

Complete the exercises, checking your answers against the key.

The truth table test of validity

So far, we have learned how to translate certain English sentences into our symbolic language, which consists of a set of constants (i.e., the capital letters that we use to represent different atomic propositions) and the truth-functional connectives. But what is the payoff of doing so? In this section we will learn what the payoff is. In short, the payoff will be that we will have a purely formal method of determining the validity of a certain class of arguments - namely, those arguments whose validity depends on the functioning of the truth- functional connectives. This is what logicians call "propositional logic" or "sentential logic".

In the first chapter, we learned the informal test of validity, which required us to try to imagine a scenario in which the premises of the argument were true and yet the conclusion false. We saw that if we can imagine such a scenario, then the argument is invalid. On the other hand, if it is not possible to imagine a scenario in which the premises are true and yet the conclusion is false, then the argument is valid. Consider this argument:

  • The convict escaped either by crawling through the sewage pipes or by hiding out in the back of the delivery truck.
  • But the convict did not escape by crawling through the sewage pipes.
  • Therefore, the convict escaped by hiding out in the back of the delivery truck.

Using the informal test of validity, we can see that if we imagine that the first premise and the second premise are true, then the conclusion must follow. However, we can also prove this argument is valid without having to imagine scenarios and ask whether the conclusion would be true in those scenarios. We can do this by a) translating this sentence into our symbolic language and then b) using a truth table to determine whether the argument is valid. Let's start with the translation. The first premise contains two atomic propositions. Here are the propositions and the constants that I'll use to stand for them:

S = The convict escaped through the sewage pipes

D = The convict escaped by hiding out in the back of the delivery van

As we can see, the first premise is a disjunction and so, using the constants indicated above, we can translate that first premise as follows:

The second premise is simply the negation of S:

Finally, the conclusion is simply the atomic sentence, D. Putting this all together in standard form, we have:

We will use the symbol "∴" to denote a conclusion and will read it "therefore".

The next thing we have to do is to construct a truth table. We have already seen some examples of truth tables when I defined the truth-functional connectives that I have introduced so far (conjunction, disjunction, and negation). A truth table (as we saw in section 2.2) is simply a device we use to represent how the truth value of a complex proposition depends on the truth of the propositions that compose it in every possible scenario. When constructing a truth table, the first thing to ask is how many atomic propositions need to be represented in the truth table. In this case, the answer is "two," since there are only two atomic propositions contained in this argument (namely, S and D). Given that there are only two atomic propositions, our truth table will contain only four rows - one row for each possible scenario. There will be one row in which both S and D are true, one row in which both S and D are false, one row in which S is true and D is false, and one row in which S is false and D is true.

The two furthest left columns are what we call the reference columns of the truth table. Reference columns assign every possible arrangement of truth values to the atomic propositions of the argument (in this case, just D and S). The reference columns capture every logically possible scenario. By doing so, we can replace having to use your imagination to imagine different scenarios (as in the informal test of validity) with a mechanical procedure that doesn't require us to imagine or even think very much at all. Thus, you can think of each row of the truth table as specifying one of the possible scenarios. That is, each row is one of the possible assignments of truth values to the atomic propositions. For example, row 1 of the truth table (the first row after the header row) is a scenario in which it is true that the convict escaped by hiding out in the back of the delivery van, and is also true that the convict escaped by crawling through the sewage pipes. In contrast, row 4 is a scenario in which the convict did neither of these things.

The next thing we need to do is figure out what the truth values of the premises and conclusion are for each row of the truth table. We are able to determine what those truth values are because we understand how the truth value of the compound proposition depends on the truth value of the atomic propositions. Given the meanings of the truth functional connectives (discussed in previous sections), we can fill out our truth table like this:

To determine the truth values for the first premise of the argument ("S v D") we just have to know the truth values of S and D and the meaning of the truth functional connective, the disjunction. The truth table for the disjunction says that a disjunction is true as long as at least one of its disjuncts is true. Thus, every row under the "S v D" column should be true, except for the last row since on the last row both D and S are false (whereas in the first three rows at least one or the other is true). The truth values for the second premise (~S) are easy to determine: we simply look at what we have assigned to "S" in our reference column and then we negate those truth values - the Ts becomes Fs and the Fs becomes Ts. That is just what I've done in the fourth column of the truth table above. Finally, the conclusion in the last column of the truth table will simply repeat what we have assigned to "D" in our reference column, since the last conclusion simply repeats the atomic proposition "D".

The above truth table is complete. Now the question is: How do we use this completed truth table to determine whether or not the argument is valid? In order to do so, we must apply what I'll call the "truth table test of validity". According to the truth table test of validity , an argument is valid if and only if for every assignment of truth values to the atomic propositions, if the premises are true then the conclusion is true. An argument is invalid if there exists an assignment of truth values to the atomic propositions on which the premises are true and yet the conclusion is false. It is imperative that you understand (and not simply memorize) what these definitions mean. You should see that these definitions of validity and invalidity have a similar structure to the informal definitions of validity and invalidity (discussed in chapter 1). The similarity is that we are looking for the possibility that the premises are true and yet the conclusion is false. If this is possible, then the argument is invalid; if it isn't possible, then the argument is valid. The difference, as I've noted above, is that with the truth table test of validity, we replace having to use your imagination with a mechanical procedure of assigning truth values to atomic propositions and then determining the truth values of the premises and conclusion for each of those assignments.

Applying these definitions to the above truth table, we can see that the argument is valid because there is no assignment of truth values to the atomic propositions (i.e., no row of our truth table) on which all the premises are true and yet the conclusion is false. Look at the first row. Is that a row in which all the premises are true and yet the conclusion false? No, it isn't, because not all the premises are true in that row. In particular, "~S" is false in that row. Look at the second row. Is that a row in which all the premises are true and yet the conclusion false? No, it isn't; although both premises are true in that row, the conclusion is also true in that row. Now consider the third row. Is that a row in which all the premises are true and yet the conclusion false? No, because it isn't a row in which both the premises are true. Finally, consider the last row. Is that a row in which all the premises are true and yet the conclusion false? Again, the answer is "no" because the premises aren't both true in that row. Thus, we can see that there is no row of the truth table in which the premises are all true and yet the conclusion is false. And that means the argument is valid.

Since the truth table test of validity is a formal method of evaluating an argument's validity, we can determine whether an argument is valid just in virtue of its form, without even knowing what the argument is about! Here is an example:

  • (A v B) v C

Here is an argument written in our symbolic language. I don't know what A, B, and C mean (i.e., what atomic propositions they stand for), but it doesn't matter because we can determine whether the argument is valid without having to know what A, B, and C mean. A, B, and C could be any atomic propositions whatsoever. If this argument form is invalid then whatever meaning we give to A, B, and C, the argument will always be invalid. On the other hand, if this argument form is valid, then whatever meaning we give to A, B, and C, the argument will always be valid.

The first thing to recognize about this argument is that there are three atomic propositions, A, B, and C. And that means our truth table will have 8 rows instead of only 4 rows like our last truth table. The reason we need 8 rows is that it takes twice as many rows to represent every logically possible scenario when we are working with three different propositions. Here is a simple formula that you can use to determine how many rows your truth table needs:

2 n (where n is the number of atomic propositions)

You read this formula "two to the n-th power". So if you have one atomic proposition (as in the truth table for negation), your truth table will have only two rows. If you have two atomic propositions, it will have four rows. If you have three atomic propositions, it will have 8 rows. The number of rows needed grows exponentially as the number of atomic propositions grows linearly. The table below represents the same relationship that the above formula does:

So, our truth table for the above argument needs to have 8 rows. Here is how that truth table looks:

Here is an important point to note about setting up a truth table. You need to make sure that your reference columns capture each distinct possible assignment of truth values. One way to make sure you do this is by following the same pattern each time you construct a truth table. There is no one right way of doing this, but here is how I do it (and recommend that you do it too). Construct the reference columns so that the atomic propositions are arranged alphabetically, from left to right. Then on the right-most reference column (the C column above), alternate true and false each row, all the way to the bottom. On the reference column to the left of that (the B column above), alternate two rows true, two rows false, all the way to the bottom. On the next column to the left (the A column above), alternate 4 true, 4 false, all the way to the bottom.

The next step is to determine the truth values of the premises and conclusion. Note that our first premise is a more complex sentence that consists of two disjunctions. The main operator is the second disjunction since the two main grouping, denoted by the parentheses, are "A v B" and "C". Notice, however, that we cannot figure out the truth values of the main operator of the sentence until we figure out the truth values of the left disjunct, "A v B". So that is where we need to start. Thus, in the truth table below, I have filled out the truth values directly underneath the "A v B" part of the sentence by using the truth values I have assigned to A and B in the reference columns. As you can see in the truth table below, each line is true except for the last two lines, which are false, since a disjunction is only false when both of the disjuncts are false. (If you need to review the truth table for disjunction, please see section 2.3).

Now, since we have figured out the truth values of the left disjunct, we can figure out the truth values under the main operator (which I have emphasized in bold in the truth table below). The two columns you are looking at to determine the truth values of the main operator are the "A v B" column that we have just figured out above and the "C" reference column to the left. It is imperative to understand that the truth values under the "A v B" are irrelevant once we have figured out the truth values under the main operator of the sentence. That column was only a means to an end (the end of determining the main operator) and so I have grayed those out to emphasize that we are no longer paying any attention to them. (When you are constructing your own truth tables, you may even want to erase these subsidiary columns once you've determined the truth values of the main operator of the sentence. Or you may simply want to circle the truth values under the main operator to distinguish them from the rest).

Finally, we will fill out the remaining two columns, which is very straightforward. All we have to do for the "~A" is negate the truth values that we have assigned to our "A" reference column. And all we have to do for the final column "C" is simply repeat verbatim the truth values that we have assigned to our reference column "C".

The above truth table is now complete. The next step is to apply the truth table test of validity in order to determine whether the argument is valid or invalid. Remember that what we're looking for is a row in which the premises are true and the conclusion is false. If we find such a row, the argument is invalid. If we do not find such a row, then the argument is valid. Applying this definition to the above truth table, we can see that the argument is invalid because of the 6th row of the table (which I have highlighted). Thus, the explanation of why this argument is invalid is that the sixth row of the table shows a scenario in which the premises are both true and yet the conclusion is false.

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Recall that a valid argument is one whose conclusion can’t possibly be false while all the premises are true. In other words, a valid argument is an argument that has no counterexamples : there are no possible combinations of truth values that make all of the argument’s premises true while also making its conclusion false.

As we have seen, one way to test an argument’s validity is to construct a truth table, which allows us to examine all of the possible truth value combinations and see whether there are any counterexamples. But constructing a truth table is tedious when an argument has more than two or three sentence letters, because the number of rows grows exponentially as the number of sentence letters increases. For example, an argument with 6 letters requires a truth table with 64 rows, and an argument with 7 letters requires a truth table with 128 rows! For obvious reasons, the truth table test of validity isn’t always practical.

Fortunately, there’s an easier way. The truth assignment test I borrow this name from Harry Gensler, who introduces the truth assignment test in his excellent book Introduction to Logic, Second Edition , pp. 133-135. He sets up the truth assignment test in a slightly different way, but the basic principle is the same. allows us to determine whether an argument is valid much more efficiently. Rather than constructing a truth table and examining all of the possible truth value combinations, we instead consider this question:

What truth values must the component propositions have in order to produce a counterexample?

To answer this question, we begin by assuming that there is a counterexample, then we try to find it by calculating the values of the sentence letters from the assumed values of the argument’s premises and conclusion. In other words, we use the following strategy:

  • Assume that the premises are all true and the conclusion is false.
  • Based on that assumption, calculate the values of as many component propositions as possible.
  • If the values of some sentence letters cannot be calculated, try all possible values for those letters to see whether any combination of truth values yields a counterexample to the argument.

If we are able to assign values to all of the sentence letters while keeping the premises true and the conclusion false, then we have found a counterexample and the argument is invalid . However, we may find that when all of the sentence letters have been calculated, some of the premises are no longer true or the conclusion is no longer false. If that happens, we can conclude that there is no counterexample and the argument is valid .

Before conducting the truth assignment test, it is helpful to arrange the premises and conclusion horizontally so that the truth values can be written beneath the connectives and sentence letters, as shown in the example below. And here’s another piece of advice. When calculating the values of component propositions, start with the propositions for which there are the fewest possible ways of assigning values to the components. For example, if any of the premises is a conjunction, that would be a good place to start, because there is only one possible way for a conjunction to be true (namely if both conjuncts are true). Similarly, if the conclusion is a disjunction, that would be a good place to start, because there is only one possible way for a disjunction to be false (namely if both disjuncts are false).

Step 1 of the truth assignment test is to assume that the premises are true and the conclusion is false. We represent this assumption by writing “1” beneath the main connective of each premise and “0” beneath the main connective of the conclusion, like this:

Step 2 is to calculate the values of as many component propositions as possible. As noted above, we should start with the propositions for which there are the fewest possible ways of assigning values to the components. There are three ways for the “⊃” in the first premise to be true, so we’ll skip over that for now. There is only one way for the “~” in the second premise to be true: the “•” must be false. Similarly, there is only one way for the “•” in the third premise to be true, namely if both conjuncts are true. And there is only one way for the “∨” in the conclusion to be false, namely if both disjuncts are false. So let’s fill in those truth values:

So far, we have determined that B is true (in the third premise) and E is false (in the conclusion). We can also see that D must be false (since ~D is true in the third premise), and A must be true (since ~A is false in the conclusion). This means that if there is a counterexample to the argument, then A and B must be true in that counterexample, and D and E must be false in that counterexample. So the counterexample, if there is one, must look like this:

Only one sentence letter remains to be calculated: the letter “C.” The first premise implies that C must be true. (The “⊃” is true and has a true antecedent, so the “≡” must be true; and since B is true, C must be true too.) However, the second premise implies that C must be false! We can’t have it both ways. If C is true, then the second premise isn’t true anymore; but if C is false, then the first premise isn’t true anymore:

So, there is no way to assign truth values to all of the sentence letters while keeping all of the premises true (and the conclusion false). In other words, there is no counterexample , and the argument is valid .

We begin by assuming that the premises are true and the conclusion is false:

Given these assumptions, the conjunction in the second premise must be false; and since ~R is false (in the conclusion), R must be true. So let’s fill in those truth values:

In the third premise, both the conditional and its antecedent are true, so the consequent must be true as well:

At this point, we can’t determine the values of any more sentence letters, so we’ll have to try all of the combinations that are possible given the values we’ve determined so far. As always, we start with the propositions for which there are the fewest possibilities. There are three ways for the disjunction in the first premise to be true, and there are three ways for the conjunction in the second premise to be false. But there are only two ways for the biconditional in the third premise to be true—namely, either P and Q are both true, or P and Q are both false. So let’s examine those two possibilities:

Notice that when P and Q are both true, the conjunction in the second premise is no longer false, and hence the negation is no longer true. So, that combination of truth values does not provide a counterexample. On the other hand, when P and Q are both false, all three premises remain true, and the conclusion remains false. So we have found a counterexample: the premises are all true and the conclusion is false in the row where P is false, Q is false, and R is true. (In that row, the truth values of the main connectives have been highlighted to make the counterexample more obvious.) Since there is a counterexample, the argument is invalid .

The truth assignment test is more efficient than the truth-table test, especially when an argument contains many sentence letters. The argument above had 3 sentence letters, so its truth table would have had 8 rows. For arguments that have more than three sentence letters, truth tables are even more cumbersome. If an argument contains six sentence letters, for instance, its truth table would require 64 rows. In cases like that, the truth assignment method can save us a lot of work!

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2.6: The Truth Table Test of Validity

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  • Page ID 26812

  • Matthew Van Cleave
  • Lansing Community College

So far, we have learned how to translate certain English sentences into our symbolic language, which consists of a set of constants (i.e., the capital letters that we use to represent different atomic propositions) and the truth-functional connectives. But what is the payoff of doing so? In this section we will learn what the payoff is. In short, the payoff will be that we will have a purely formal method of determining the validity of a certain class of arguments—namely, those arguments whose validity depends on the functioning of the truth-functional connectives. This is what logicians call “propositional logic” or “sentential logic.”

In the first chapter, we learned the informal test of validity, which required us to try to imagine a scenario in which the premises of the argument were true and yet the conclusion false. We saw that if we can imagine such a scenario, then the argument is invalid. On the other hand, if it is not possible to imagine a scenario in which the premises are true and yet the conclusion is false, then the argument is valid. Consider this argument:

  • The convict escaped either by crawling through the sewage pipes or by hiding out in the back of the delivery truck.
  • But the convict did not escape by crawling through the sewage pipes.
  • Therefore, the convict escaped by hiding out in the back of the delivery truck.

Using the informal test of validity, we can see that if we imagine that the first premise and the second premise are true, then the conclusion must follow. However, we can also prove this argument is valid without having to imagine scenarios and ask whether the conclusion would be true in those scenarios. We can do this by a) translating this sentence into our symbolic language and then b) using a truth table to determine whether the argument is valid. Let’s start with the translation. The first premise contains two atomic propositions. Here are the propositions and the constants that I’ll use to stand for them:

S = The convict escaped through the sewage pipes

D = The convict escaped by hiding out in the back of the delivery van

As we can see, the first premise is a disjunction and so, using the constants indicated above, we can translate that first premise as follows:

The second premise is simply the negation of S:

Finally, the conclusion is simply the atomic sentence, D. Putting this all together in standard form, we have:

We will use the symbol “∴“ to denote a conclusion and will read it “therefore.”

The next thing we have to do is to construct a truth table. We have already seen some examples of truth tables when I defined the truth-functional connectives that I have introduced so far (conjunction, disjunction, and negation). A truth table (as we saw in section 2.2) is simply a device we use to represent how the truth value of a complex proposition depends on the truth of the propositions that compose it in every possible scenario. When constructing a truth table, the first thing to ask is how many atomic propositions need to be represented in the truth table. In this case, the answer is “two,” since there are only two atomic propositions contained in this argument (namely, S and D). Given that there are only two atomic propositions, our truth table will contain only four rows—one row for each possible scenario. There will be one row in which both S and D are true, one row in which both S and D are false, one row in which S is true and D is false, and one row in which S is false and D is true.

The two furthest left columns are what we call the reference columns of the truth table. Reference columns assign every possible arrangement of truth values to the atomic propositions of the argument (in this case, just D and S). The reference columns capture every logically possible scenario. By doing so, we can replace having to use your imagination to imagine different scenarios (as in the informal test of validity) with a mechanical procedure that doesn’t require us to imagine or even think very much at all. Thus, you can think of each row of the truth table as specifying one of the possible scenarios. That is, each row is one of the possible assignments of truth values to the atomic propositions. For example, row 1 of the truth table (the first row after the header row) is a scenario in which it is true that the convict escaped by hiding out in the back of the delivery van, and is also true that the convict escaped by crawling through the sewage pipes. In contrast, row 4 is a scenario in which the convict did neither of these things.

The next thing we need to do is figure out what the truth values of the premises and conclusion are for each row of the truth table. We are able to determine what those truth values are because we understand how the truth value of the compound proposition depends on the truth value of the atomic propositions. Given the meanings of the truth functional connectives (discussed in previous sections), we can fill out our truth table like this:

To determine the truth values for the first premise of the argument (“S v D”) we just have to know the truth values of S and D and the meaning of the truth functional connective, the disjunction. The truth table for the disjunction says that a disjunction is true as long as at least one of its disjuncts is true. Thus, every row under the “S v D” column should be true, except for the last row since on the last row both D and S are false (whereas in the first three rows at least one or the other is true). The truth values for the second premise (~S) are easy to determine: we simply look at what we have assigned to “S” in our reference column and then we negate those truth values—the Ts becomes Fs and the Fs becomes Ts. That is just what I’ve done in the fourth column of the truth table above. Finally, the conclusion in the last column of the truth table will simply repeat what we have assigned to “D” in our reference column, since the last conclusion simply repeats the atomic proposition “D.”

The above truth table is complete. Now the question is: How do we use this completed truth table to determine whether or not the argument is valid? In order to do so, we must apply what I’ll call the “truth table test of validity.” According to the truth table test of validity , an argument is valid if and only if for every assignment of truth values to the atomic propositions, if the premises are true then the conclusion is true. An argument is invalid if there exists an assignment of truth values to the atomic propositions on which the premises are true and yet the conclusion is false. It is imperative that you understand (and not simply memorize) what these definitions mean. You should see that these definitions of validity and invalidity have a similar structure to the informal definitions of validity and invalidity (discussed in chapter 1). The similarity is that we are looking for the possibility that the premises are true and yet the conclusion is false. If this is possible, then the argument is invalid; if it isn’t possible, then the argument is valid. The difference, as I’ve noted above, is that with the truth table test of validity, we replace having to use your imagination with a mechanical procedure of assigning truth values to atomic propositions and then determining the truth values of the premises and conclusion for each of those assignments.

Applying these definitions to the above truth table, we can see that the argument is valid because there is no assignment of truth values to the atomic propositions (i.e., no row of our truth table) on which all the premises are true and yet the conclusion is false. Look at the first row. Is that a row in which all the premises are true and yet the conclusion false? No, it isn’t, because not all the premises are true in that row. In particular, “~S” is false in that row. Look at the second row. Is that a row in which all the premises are true and yet the conclusion false? No, it isn’t; although both premises are true in that row, the conclusion is also true in that row. Now consider the third row. Is that a row in which all the premises are true and yet the conclusion false? No, because it isn’t a row in which both the premises are true. Finally, consider the last row. Is that a row in which all the premises are true and yet the conclusion false? Again, the answer is “no” because the premises aren’t both true in that row. Thus, we can see that there is no row of the truth table in which the premises are all true and yet the conclusion is false. And that means the argument is valid.

Since the truth table test of validity is a formal method of evaluating an argument’s validity, we can determine whether an argument is valid just in virtue of its form, without even knowing what the argument is about! Here is an example:

  • (A v B) v C

Here is an argument written in our symbolic language. I don’t know what A, B, and C mean (i.e., what atomic propositions they stand for), but it doesn’t matter because we can determine whether the argument is valid without having to know what A, B, and C mean. A, B, and C could be any atomic propositions whatsoever. If this argument form is invalid then whatever meaning we give to A, B, and C, the argument will always be invalid. On the other hand, if this argument form is valid, then whatever meaning we give to A, B, and C, the argument will always be valid.

The first thing to recognize about this argument is that there are three atomic propositions, A, B, and C. And that means our truth table will have 8 rows instead of only 4 rows like our last truth table. The reason we need 8 rows is that it takes twice as many rows to represent every logically possible scenario when we are working with three different propositions. Here is a simple formula that you can use to determine how many rows your truth table needs:

2n (where n is the number of atomic propositions)

You read this formula “two to the n-th power.” So if you have one atomic proposition (as in the truth table for negation), your truth table will have only two rows. If you have two atomic propositions, it will have four rows. If you have three atomic propositions, it will have 8 rows. The number of rows needed grows exponentially as the number of atomic propositions grows linearly. The table below represents the same relationship that the above formula does:

So, our truth table for the above argument needs to have 8 rows. Here is how that truth table looks:

Here is an important point to note about setting up a truth table. You need to make sure that your reference columns capture each distinct possible assignment of truth values. One way to make sure you do this is by following the same pattern each time you construct a truth table. There is no one right way of doing this, but here is how I do it (and recommend that you do it too). Construct the reference columns so that the atomic propositions are arranged alphabetically, from left to right. Then on the right-most reference column (the C column above), alternate true and false each row, all the way to the bottom. On the reference column to the left of that (the B column above), alternate two rows true, two rows false, all the way to the bottom. On the next column to the left (the A column above), alternate 4 true, 4 false, all the way to the bottom.

The next step is to determine the truth values of the premises and conclusion. Note that our first premise is a more complex sentence that consists of two disjunctions. The main operator is the second disjunction since the two main grouping, denoted by the parentheses, are “A v B” and “C”. Notice, however, that we cannot figure out the truth values of the main operator of the sentence until we figure out the truth values of the left disjunct, “A v B.” So that is where we need to start. Thus, in the truth table below, I have filled out the truth values directly underneath the “A v B” part of the sentence by using the truth values I have assigned to A and B in the reference columns. As you can see in the truth table below, each line is true except for the last two lines, which are false, since a disjunction is only false when both of the disjuncts are false. (If you need to review the truth table for disjunction, please see section 2.3.)

Now, since we have figured out the truth values of the left disjunct, we can figure out the truth values under the main operator (which I have emphasized in bold in the truth table below). The two columns you are looking at to determine the truth values of the main operator are the “A v B” column that we have just figured out above and the “C” reference column to the left. It is imperative to understand that the truth values under the “A v B” are irrelevant once we have figured out the truth values under the main operator of the sentence. That column was only a means to an end (the end of determining the main operator) and so I have grayed those out to emphasize that we are no longer paying any attention to them. (When you are constructing your own truth tables, you may even want to erase these subsidiary columns once you’ve determined the truth values of the main operator of the sentence. Or you may simply want to circle the truth values under the main operator to distinguish them from the rest.)

Finally, we will fill out the remaining two columns, which is very straightforward. All we have to do for the “~A” is negate the truth values that we have assigned to our “A” reference column. And all we have to do for the final column “C” is simply repeat verbatim the truth values that we have assigned to our reference column “C.”

The above truth table is now complete. The next step is to apply the truth table test of validity in order to determine whether the argument is valid or invalid. Remember that what we’re looking for is a row in which the premises are true and the conclusion is false. If we find such a row, the argument is invalid. If we do not find such a row, then the argument is valid. Applying this definition to the above truth table, we can see that the argument is invalid because of the 6th row of the table (which I have highlighted). Thus, the explanation of why this argument is invalid is that the sixth row of the table shows a scenario in which the premises are both true and yet the conclusion is false.

Use the truth table test of validity to determine whether or not the following arguments are valid or invalid.

1. 1. A v B 2. B 3. ∴ ~A

2. 1. A ⋅ B 2. ∴ A v B

3. 1. ~C 2. ∴ ~(C v A)

4. 1. (A v B) ⋅ (A v C) 2. ~A 3. ∴ B v C

5 . 1. R ⋅ (T v S) 2. T 3. ∴ ~S

6 . 1. A v B 2. ∴ A ⋅ B

7. 1. ~(A ⋅ B) 2. ∴ ~A v ~B

8. 1. ~(A v B) 2. ∴ ~A v ~B

9. 1. (R v S) ⋅ ~D 2. ~R 3. ∴ S ⋅ ~D

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Wage assignment and employers’ responsibilities

Business Management Daily Editors

Tough economic times raise some tricky HR issues—for example, when an employee’s financial straits begin to affect his employer.

Must we honor a payday loan wage assignment?

Q. An employee borrowed money from a payday loan service at a very high interest rate that I feel is unfair. The payday loan service sent me a “wage assignment” notice and told me that our company must withhold money from his paychecks.  What is a wage assignment, and does our company actually have to honor it? A. A wage assignment is a document that allows a creditor to attach part of the employee’s wages if the employee fails to pay a specific debt. The creditor does not have to obtain a judgment in a court proceeding before requesting payment. Under the Illinois Wage Assignment Act (740 ILCS 170), private employers are obligated to honor a creditor’s properly served demand for a valid wage assignment, unless an employee presents a timely, valid , written defense to the wage assignment.

What constitutes a valid assignment?

Q. How can I tell if a wage assignment is valid? How long is it valid? A. A valid wage assignment document must have the words “Wage Assignment” printed or written in boldface letters of not less than ¼ inch in height at the head of the wage assignment and one inch above or below the line where the employee signs the assignment. The employee must have signed the document in person, and the document must show the date of execution, the employee’s Social Security number, the name of the employer at the time of execution, the amount of money loaned or the price of the articles sold or other consideration given, the rate of interest or time-price differential to be paid, if any, and the date on which such payments are due. A wage assignment is valid for no more than three years after the employee signs it and the employer’s name appears on it. If the employee changes jobs, the wage assignment is valid for two years, even though the new employer’s name does not appear on the assignment.

Handling wage assignments

Q. How does the wage assignment process start? A. Assuming that the wage assignment document complies with the formal requirements, the creditor must serve “demand to withhold” on the employer. The demand is valid only if:

The employee has defaulted on the debt secured by the assignment for more than 40 days, and the default has continued to the date of the demand.

The demand contains a correct statement of the amount the employee is in default, and the creditor provides an original or a photocopy of the assignment to the employer.

The creditor has served a “notice of intention to make the demand” upon the employee, with a copy to the employer, by registered or certified mail not less than 20 days before serving the demand.

Putting on the brakes

Q. Can an employee stop the wage assignment process? A. The employee does have a right to contest the demand. If an employee has a legal defense to the wage assignment, the employee may—within 20 days after receiving a notice of demand or within five days after the employer is served with the demand—notify the employer, in writing, of any defense to the wage assignment and send a copy of the written defense to the creditor by registered or certified mail.   As a result, the employee’s wages are not subject to a demand served by the creditor unless the employer receives a copy of a subsequent written agreement between the creditor and the employee authorizing such payments. Similarly, if the creditor receives a copy of the defense prior to serving its demand upon the employer, the creditor may not serve the demand upon the employer.  Whether the employee’s defense is legally valid is not an issue the employer must resolve. Instead, the employee and the creditor may attempt to reach another agreement or the creditor may simply bring a separate lawsuit against the employee to collect an outstanding debt. 

BP Handbook D

Calculating the wage assignment payment

Q. How much must the employer withhold—and when? A. The employer must begin payment to the creditor no sooner than five business days after service of such a demand.  The employer must withhold the lesser of:

15% of weekly gross wages

The amount by which the disposable earnings for a week (pay remaining after federal and state taxes, Social Security deductions and any other amounts required by law to be withheld, including required retirement contributions) exceed 45 times the federal minimum wage, unless a notice of defense is received within that five-day period.

The employer shall be paid a fee of $12 for each wage assignment. That $12 is credited against the debt.

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Question : 11.An assignment valid only if: a.it in a particular form. b.it written. c.there : 1780885

11. An assignment is valid only if:

a. it is in a particular form.

b. it is written.

c. there is a manifestation of the intent to assign.

d. the assignment is paid for by the assignee.

12. Generally, it is easiest to assign:

b. personal services.

d. all of the above.

13. The right to performance under a contract can be assigned:

a. if the burden of performance is not materially increased.

b. if the contract requires the performance of personal services.

c. if the contract provides for the extension of credit.

14. In general, an assignee stands:

a. in a position subordinate to the assignor.

b. exactly in the position of the assignor.

c. in a position superior to the assignor.

d. in a position similar to, but not equal to, the assignor.

15. The making of an assignment __________ the assignor of any obligation of the contract.

a. relieves

b. conditionally relieves

c. does not relieve

d. discharges

16. If an obligor could successfully defend against a suit brought by the assignor:

a. the obligor will also prevail against the third-party beneficiary.

b. the obligor will also prevail against the assignee.

c. the obligor will also prevail against the incidental beneficiary.

d. none of the above.

17. The substitution of an old contract for a new one that replaces an obligation or a party for another is a:

a. novation.

b. warranty.

c. assignment.

d. delegation of duties.

18. An obligor may delegate his or her duties to perform under a contract when the:

a. performance of the duty is standardized and nonpersonal.

b. obligor is unable to perform his or her duties.

c. contract is silent as to the right of assignment.

d. obligor is an expert in his or her specialized duties under the contract.

19. Unless language or circumstances indicate the contrary,  a general assignment is:

a. a transfer of property only.

b. both a transfer of rights and a delegation of duties.

c. a delegation of duties only.

d. a transfer of rights only.

20. The delegator of construction duties remains liable if:

a. the delegatee performs the work properly, but the obligee did not approve of the delegation.

b. the delegatee performs the work improperly.

c. the obligee objects in writing to the delegatee’s performance of the work, even if the delegatee performs the work properly.

d. the value of the contract is $500 or more and the delegatee performs the work properly.

Solution 5 (1 Ratings )

  • CASE 1.A professor owned a home next door to a very dilapidated, neglected home. John Cataldo purchased the home next door and made a contract with...
  • TRUE/FALSE 1.Generally, contracts are discharged by the performance of the terms of the contract. 2.A condition precedent must occur before a party to a c...
  • 11.A party who in good faith has provided substandard performance of a contract may sue to recover the payment specified in the contract. 12.The doctrine of...
  • 21.In a mutual rescission, both parties, acting in good faith, renew their commitment to perform all obligations set forth in their original agreement. 22.For the...
  • MULTIPLE CHOICE 1.A __________ is a condition that must occur before a party to a contract has an obligation to perform under a contract. a.condition prec...
  • 11.Through which of the following circumstances may a contract be discharged? a.mutual cancellation b.mutual rescission c.accord and satisfaction ...
  • CASE 1.An art collector commissioned an artist to create a sculpture for the collector. The artist wanted a substantial amount of money for the sculpture. This...
  • TRUE/FALSE 1.When one party breaks the contract, the contract is said to be breached. 2.When a party expressly declares before the time for performance ar...
  • 11.The measure of monetary damages when there has been a breach of contract is the sum of money that will place the injured party in...
  • 21.A party must mitigate damages at all costs. 22.When one party commits a non-material breach of contract, the other party may rescind the contract. 23.An injured party....

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Is multiple assignment less efficient?

Consider the following:

Will that actually be less efficient than this:

I heard a mention of multiple assignment entailing ‘temporary registers’ but is the same true for single assignment?

I did a quick benchmark and it appears multiple assignment is very marginally faster, especially when assigning to multiple global variables or something. Any idea why that might be? I was expecting it to be identically fast or even slightly slower.

Mini disclaimer: I haven’t had the time to properly dive into how the parser handles assignments.

Short answer: standalone assignment is a bit faster than parallel assignment - a couple of times, the latter gets slower with more assignments.

Mind sharing your benchmark? I’m positive there must have been a hidden factor involved.

As far as I know you’re right and both vanilla Lua and Luau have these temporary registers where results from evaluation of the right hand side are stored before the values are assigned. Furthermore, I remember zeuxcg mentioning that multiple assignments are more optimised when no destruction is taking place (like table unpacking).

Should this knowledge affect the way you code?

Certainly not! The difference is so negligible in the grand scheme of things that the decision about using it, except in extreme cases, is based solely on your readability preferences.

That takes about 0.12 seconds.

That takes about 0.16 seconds.

Sorry for the late reply. Looks like some other optimisation was applied in my benchmark.

The result is quite surprising to me, maybe it has something to do with:

There should still be some copying from temp registries happening under the hood on the cpp side though.

Edit. @asadefa also found this:

image

Also, out of curiosity, are you going off my numbers, or did you run also run my benchmark yourself? Were you able to replicate my results?

I could repo the difference, except I also switched to os.clock() and tried with even more vars in which case the difference was less noticeable. Also, I later localised them.

Re the edit: So basically, what that means to me, is some times performing the assignments in a certain order could be more efficient, e.g., for cache efficiency reasons or something. Multiple assignment basically leaves the order unspecified and able to be optimized, but doing them one at a time forces them to be performed in a specific, possibly sub-optimal order.

IMAGES

  1. Solved Assume the following assignment is valid and does not

    an assignment is valid only if

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    an assignment is valid only if

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    an assignment is valid only if

  4. Everything You Need to Know About Assignment Structure

    an assignment is valid only if

  5. What is an Assignment and how to prepare it?

    an assignment is valid only if

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    an assignment is valid only if

VIDEO

  1. Choose the INCORRECT statements from the following

  2. SE03 04 Type of Exceptions

  3. Explaining the if statement assignment

  4. Incorrect statement to correct statement #ytshorts #shortvideo #shorts #viral

  5. Select the correct statement

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COMMENTS

  1. Accounting Law chapter 17 multiple choice Flashcards

    Law Accounting Law chapter 17 multiple choice 5.0 (1 review) A third-party beneficiary: a. may be obligated to pay for services rendered. b. may bring suit on and enforce the contract. c. must consent to the contract. d. must be identified by name. Click the card to flip 👆 B Click the card to flip 👆 1 / 20 Flashcards Learn Test Match Q-Chat

  2. Ch 18 MC Flashcards

    An assignment: is a transfer of rights. When a buyer assigns the right to goods under a contract, the buyer's liability to make payment to the seller is: still in effect. An assignment is valid only if: there is a manifestation of the intent to assign. Generally, it is easiest to assign: money.

  3. Assignments: The Basic Law

    An assignment is the transfer of rights held by one party called the "assignor" to another party called the "assignee." The legal nature of the assignment and the contractual terms of the agreement between the parties determines some additional rights and liabilities that accompany the assignment.

  4. Validity of a Contract Assignment

    At No Cost! What Is a Contract? A contract is a legally binding arrangement between two or more parties. A contract supplies particulars of what the parties agree to perform or exchange. A contract may be in written or oral form. In most cases, to be legally binding, a contract must be in writing and signed by all parties concerned.

  5. bul 2241 ch 17 Flashcards

    Unless language or circumstances indicate the contrary, a general assignment is: a. a delegation of duties only. b. a transfer of property only. c. a transfer of rights only. d. both a transfer of rights and a delegation of duties. Click the card to flip 👆 both a transfer of rights and a delegation of duties Click the card to flip 👆 1 / 10

  6. Legal Assignment: Everything You Need to Know

    A valid legal assignment only occurs when all underlying elements of a lawfully binding contract are included in it, including intent. A trial court can determine if an assignment has occurred. To prevent disputes or miscommunications, it's important that the subject matter is clearly identified in the assignment.

  7. Introduction to Logic

    A sentence is valid if and only if it is satisfied by every truth assignment. For example, the sentence ( p ∨ ¬ p) is valid. If a truth assignment makes p true, then the first disjunct is true and the disjunction as a whole true. If a truth assignment makes p false, then the second disjunct is true and the disjunction as a whole is true.

  8. Assignment of Contract: What Is It? How It Works

    The Letter of Assignment must include details about who is to take over the contractual obligations of the exiting party and when the transfer will take place. If the assignment is valid, the assignor is not required to obtain the consent or signature of the other parties to the original contract for the valid assignment to take place.

  9. Assignee & Assignor

    Updated: 11/21/2023 Table of Contents What is Assignment? Assignee Definition Assignor Definition Obligor vs. Obligee Breaches and Defenses Lesson Summary Frequently Asked Questions Is the...

  10. Understanding an assignment and assumption agreement

    The party making the assignment is called the assignor, while the third party accepting the assignment is known as the assignee. In order for an assignment and assumption agreement to be valid, the following criteria need to be met: The initial contract must provide for the possibility of assignment by one of the initial contracting parties.

  11. The Logic of "If" vs. "Only if" (article)

    The only time I wear a hat is if it's sunny. Only sunny days will get me to wear a hat. Notice that the placement of "only" in relation to "sunny" is quite different in each statement, and the order of the elements "hat" and "sunny" are different as well. However, logically, all four of these statements mean the same thing! if ...

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    Signing. An assignment of a UK patent (or application) must be in writing and signed by the assignor. It used to be the case that an assignment of a UK patent (or application) would need to be ...

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    any attempted assignment is wholly void, except in those cases in which a prescribed mode for making the assignment exists, and then it is valid only if the prescribed method be followed. The contract, however, as between the original parties to it is in no manner invalidated by the mere fact of an assignment in violation of the stipulation. 3.

  14. Truth Tables: The truth table test of validity

    F. The above truth table is now complete. The next step is to apply the truth table test of validity in order to determine whether the argument is valid or invalid. Remember that what we're looking for is a row in which the premises are true and the conclusion is false. If we find such a row, the argument is invalid.

  15. Contractual Provision Limiting or Prohibiting Assignment

    Anti-assignment clauses are effective only if they contain clear, unambiguous language of prohibition. ... If a party attempts to assign contractual rights but does not do so in conformance with the contractual terms, the assignment is valid if the contract rights assigned will not be affected by a change in the personal character of the party ...

  16. Necessity for a Writing; Oral Assignments

    Pursuant to Restat 2d of Contracts, § 324, an assignor's intention to assign a right can be made either orally or in writing, unless a writing is required by a statute or by contract. In cases before a court of law, an oral assignment is ineffective to prove the right of an assignee. [iv] [i] Kelly v.

  17. The truth assignment test of validity

    The Truth Assignment Test for Validity. Recall that a valid argument is one whose conclusion can't possibly be false while all the premises are true. In other words, a valid argument is an argument that has no counterexamples: there are no possible combinations of truth values that make all of the argument's premises true while also making its conclusion false.

  18. Contracts

    Preview Business Law Ch 20 40 terms ian_macdonald1 Preview Terms in this set (10) Is the assignment valid when there is an anti-assignment clause? Assignment is valid even though there is an anti-assignment provision, unless it substantially changes the obligor's duty or risk or prohibited by law. what makes the assignment ineffective?

  19. 2.6: The Truth Table Test of Validity

    The above truth table is now complete. The next step is to apply the truth table test of validity in order to determine whether the argument is valid or invalid. Remember that what we're looking for is a row in which the premises are true and the conclusion is false. If we find such a row, the argument is invalid.

  20. Why would you use an assignment in a condition?

    The reason is: Performance improvement (sometimes) Less code (always) Take an example: There is a method someMethod () and in an if condition you want to check whether the return value of the method is null. If not, you are going to use the return value again. If(null != someMethod()){.

  21. Wage assignment and employers' responsibilities

    The demand is valid only if: The employee has defaulted on the debt secured by the assignment for more than 40 days, and the default has continued to the date of the demand.

  22. Solved > 11.An assignment is valid only if: a.it is:1780885 ...

    An assignment is valid only if: a. it is in a particular form. b. it is written. c. there is a manifestation of the intent to assign. d. the assignment is paid for by the assignee. 12. Generally, it is easiest to assign: a. credit. b. personal services. c. money. d. all of the above. 13. The right to performance under a contract can be assigned:

  23. Bus Law Exam 4

    An assignment is valid only if: a. it is in a particular form. b. it is written. c. there is a manifestation of the intent to assign. d. the assignment is paid for by the assignee. Feedback c An incidental beneficiary of a contract: a. can sue to enforce the contract. b.cannot sue to enforce the contract.

  24. Is multiple assignment less efficient?

    Consider the following: unrelated1, unrelated2 = 1, "Hello" Will that actually be less efficient than this: unrelated1 = 1 unrelated2 = "Hello" I heard a mention of multiple assignment entailing 'temporary registers'…